B.Arch

You can appear in JEE Mains paper 1and paper 2 . Paper 1 is for B.Tech and paper 2 for B.Arch. Start preparing .
All the best.

Yes, NATA is the only way to get into Shibpur BE college for B.Arch.

Qualification
NATA
Age
Maximum 21 years
Other eligibility criteria
Candidate must have passed 10+2 with Mathematics as a subject
OR
10+3 Diploma (any stream) recognized by Central/ State Governments
OR
International Baccalaureate Diplomas, after 10 years of schooling, and with Mathematics as compulsory subject of examination

Please refer to the link provided below for a detailed list of colleges which offers B.Arch courses in India. You should be able to navigate to a college of your choice using the filters on the web page. Additionally, download their brochure for further details.
Regards.
https://www.shiksha.com/architecture-planning/colleges/b-arch-colleges-india

Yes, you can study B.Arch via distance education. Any candidate who is having HSC pass certificate from recognised institute is eligible for this course. However, few institute conduct entrance exam for admission to this course, so be sure to confirm with the admission authorities about the eligibility criteria for this course from their institute. Regards.

Yes, NATA is cumpolsary for getting into an architecture school you have to have minimum 40% marks in NATA. Check the link below:
https://www.shiksha.com/architecture-planning/course/b-arch-dayananda-sagar-college-of-engineering-dsce-banashankari-bangalore-236760